Finite Group Databasebeta

← #13058528

Subgroups — #13058528

Order 1344.

520 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10621368C211yesmaximal, characteristic, complemented
2C7×#882C211yesmaximal, characteristic, complemented
3C3×#6448C211yesmaximal, characteristic, complemented
4#10621139C211yesmaximal, characteristic, complemented
5#10621132C211yesmaximal, characteristic, complemented
6#10621130C211yesmaximal, characteristic, complemented
7#10621087C211yesmaximal, characteristic, complemented
8#10621037C211yesmaximal, characteristic, complemented
9#10621037C211yesmaximal, characteristic, complemented
10#10621026C211yesmaximal, characteristic, complemented
11#10621024C211yesmaximal, characteristic, complemented
12#10620935C211yesmaximal, characteristic, complemented
13#10620932C211yesmaximal, characteristic, complemented
14#10620912C211yesmaximal, characteristic, complemented
15#10620888C211yesmaximal, characteristic, complemented
16#90285—31nomaximal, Hall
17C23×D3×C7C2211yescharacteristic, complemented
18C22×D3×D7C2211yescharacteristic, complemented
19C2×#4268C2211yescharacteristic
20C2×Dic42C2211yescharacteristic, complemented
21C2×C7×#67C2211yescharacteristic
22C2×C7×D12C2211yescharacteristic
23C2×C7×D12C2211yescharacteristic
24C2×C3×C22⋊D7C2211yescharacteristic
25C2×C3×Dic14C2211yescharacteristic, complemented
26C2×#4248C2211yescharacteristic, complemented
27C2×#4247C2211yescharacteristic
28C2×#4247C2211yescharacteristic
29C2×#4245C2211yescharacteristic
30C2×#4245C2211yescharacteristic
31C3×C7×C22⋊C4C2211yescharacteristic, complemented
32#66636C2211yescharacteristic, complemented
33#66631C2211yescharacteristic, complemented
34#66631C2211yescharacteristic, complemented
35C4×Dic21C2211yescharacteristic, complemented
36C7×(C2×D3)⋊C4C2211yescharacteristic, complemented
37C7×(C2×D3)⋊C4C2211yescharacteristic, complemented
38C3×C22⋊Dic7C2211yescharacteristic, complemented
39C3×(C2×D7)⋊C4C2211yescharacteristic, complemented
40C3×(C2×D7)⋊C4C2211yescharacteristic, complemented
41C3×C4×Dic7C2211yescharacteristic, complemented
42#66575C2211yescharacteristic, complemented
43(C2×D3)⋊Dic7C2211yescharacteristic, complemented
44(C2×D3)⋊Dic7C2211yescharacteristic, complemented
45(C2×D3)⋊Dic7C2211yescharacteristic, complemented
46(C2×D3)⋊Dic7C2211yescharacteristic, complemented
47(C2×D3)⋊Dic7C2211yescharacteristic, complemented
48(C2×D3)⋊Dic7C2211yescharacteristic, complemented
49(C2×D3)⋊Dic7C2211yescharacteristic, complemented
50(C2×D7)⋊Dic3C2211yescharacteristic, complemented
51Dic3×Dic7C2211yescharacteristic, complemented
52C7×#120—31no—
53#6516—31no—
54#6516—31no—
55#6500—31no—
56#6500—31no—
57#6500—31no—
58#6499—31no—
59#6499—31no—
60#6499—31no—
61#6448—31no—
62#6448—31no—
63#6448—31no—
64#6448—31no—
65#6448—31no—
66#6448D311yescharacteristic, complemented
67#5683—71nomaximal, Hall
68C23×C3×C7C2311yescharacteristic
69C22×D21C2311yescharacteristic
70C22×D3×C7—41no—
71C22×D3×C7—41no—
72C22×D3×C7—41no—
73C22×D3×C7C2311yescharacteristic
74C22×D3×C7C2311yescharacteristic
75C22×D3×C7C2311yescharacteristic
76C22×C3×D7C2311yescharacteristic
77C2×D3×D7—41no—
78C2×D3×D7—41no—
79C2×D3×D7—41no—
80C2×C3×C4×C7C2311yescharacteristic
81C2×C3×C4×C7C2311yescharacteristic
82#4268—41no—
83C2×Dic21C2311yescharacteristic
84C2×Dic21C2311yescharacteristic
85C2×Dic21C2311yescharacteristic
86Dic42—41no—
87C7×#67—41no—
88C2×C7×Dic3C2311yescharacteristic
89C7×D12—41no—
90C7×D12—41no—
91C3×C22⋊D7—41no—
92C2×C3×Dic7C2311yescharacteristic
93C2×C3×Dic7C2311yescharacteristic
94C2×C3×Dic7C2311yescharacteristic
95C3×Dic14—41no—
96#4248—41no—
97#4247—41no—
98#4247—41no—
99#4245—41no—
100#4245—41no—
101C24×C7—31no—
102C23×D7—31no—
103C2×C7×D4—31no—
104C2×C7×D4—31no—
105C2×C7×D4—31no—
106C2×C22⋊D7—31no—
107C2×C22⋊D7—31no—
108C2×C22⋊D7—31no—
109C2×C22⋊D7—31no—
110C2×C22⋊D7—31no—
111C2×C22⋊D7C2×D311yescharacteristic
112C2×Dic14—31no—
113C2×Dic14—31no—
114C2×Dic14C2×D311yescharacteristic, complemented
115C7×C22⋊C4—31no—
116C7×C22⋊C4—31no—
117C7×C22⋊C4C2×D311yescharacteristic, complemented
118C22⋊Dic7—31no—
119C22⋊Dic7—31no—
120C22⋊Dic7—31no—
121C22⋊Dic7—31no—
122C22⋊Dic7—31no—
123C22⋊Dic7—31no—
124C22⋊Dic7—31no—
125C22⋊Dic7—31no—
126C22⋊Dic7C2×D311yescharacteristic, complemented
127(C2×D7)⋊C4—31no—
128(C2×D7)⋊C4—31no—
129(C2×D7)⋊C4—31no—
130(C2×D7)⋊C4—31no—
131(C2×D7)⋊C4C2×D311yescharacteristic, complemented
132(C2×D7)⋊C4C2×D311yescharacteristic, complemented
133C4×Dic7—31no—
134C4×Dic7—31no—
135C4×Dic7C2×D311yescharacteristic, complemented
136C3×#124—71no—
137#947—71no—
138#947—71no—
139#937—71no—
140#937—71no—
141#885—71no—
142#885—71no—
143#885—71no—
144#885—71no—
145#882—71no—
146#882—71no—
147#882—71no—
148#882D711yescharacteristic, complemented
149#875—71no—
150#875—71no—
151C22×C3×C7—21no—
152C22×C3×C7—21no—
153C22×C3×C7—21no—
154C22×C3×C7C2411yescharacteristic
155C2×D21—21no—
156C2×D21—21no—
157C2×D21—21no—
158C2×D3×C7—21no—
159C2×D3×C7—21no—
160C2×D3×C7—21no—
161C2×D3×C7—21no—
162C2×D3×C7—21no—
163C2×D3×C7—21no—
164C2×D3×C7—21no—
165C2×D3×C7—21no—
166C2×D3×C7—21no—
167C2×D3×C7—44no—
168C2×C3×D7—21no—
169C2×C3×D7—21no—
170C2×C3×D7—21no—
171D3×D7—44no—
172C3×C4×C7—21no—
173C3×C4×C7—21no—
174Dic21—21no—
175Dic21—21no—
176Dic21—21no—
177C3×Dic7—21no—
178C3×Dic7—21no—
179C3×Dic7—21no—
180C7×Dic3—21no—
181H(3,𝔽4)—211noSylow
182C23×C7—31no—
183C23×C7—31no—
184C23×C7—31no—
185C23×C7—121no—
186C23×C7—121no—
187C23×C7—121no—
188C23×C7C22×D311yescharacteristic
189C22×D7—31no—
190C22×D7—121no—
191C22×D7—121no—
192C22×D7—121no—
193C22×D7C22×D311yescharacteristic
194C7×D4—121no—
195C7×D4—121no—
196C7×D4—121no—
197C2×C4×C7—31no—
198C2×C4×C7C22×D311yescharacteristic
199C2×C4×C7C22×D311yescharacteristic
200C22⋊D7—41no—
201C22⋊D7—121no—
202C22⋊D7—121no—
203C22⋊D7—121no—
204C22⋊D7—121no—
205C22⋊D7—121no—
206C2×Dic7—31no—
207C2×Dic7—31no—
208C2×Dic7—31no—
209C2×Dic7C22×D311yescharacteristic
210C2×Dic7C22×D311yescharacteristic
211C2×Dic7C22×D311yescharacteristic
212Dic14—41no—
213Dic14—121no—
214Dic14—121no—
215C23×D3—71no—
216C23×D3C2×D711yescharacteristic, complemented
217C2×C3×Q8—71no—
218C2×C3×D4—71no—
219C2×#67—71no—
220C2×#67—71no—
221C2×#67—71no—
222C2×#67C2×D711yescharacteristic
223C2×D12—71no—
224C2×D12—71no—
225C2×D12C2×D711yescharacteristic
226C2×D12C2×D711yescharacteristic
227C2×Dic6—71no—
228C2×Dic6—71no—
229C3×C22⋊C4—71no—
230C3×C22⋊C4—71no—
231C3×C22⋊C4—71no—
232C3×C22⋊C4C2×D711yescharacteristic, complemented
233C3×C42—71no—
234#217—71no—
235#217—71no—
236(C2×D3)⋊C4—71no—
237(C2×D3)⋊C4—71no—
238(C2×D3)⋊C4—71no—
239(C2×D3)⋊C4—71no—
240(C2×D3)⋊C4—71no—
241(C2×D3)⋊C4—71no—
242(C2×D3)⋊C4—71no—
243(C2×D3)⋊C4—71no—
244(C2×D3)⋊C4—71no—
245(C2×D3)⋊C4—71no—
246(C2×D3)⋊C4C2×D711yescharacteristic, complemented
247(C2×D3)⋊C4C2×D711yescharacteristic, complemented
248C4×Dic3—71no—
249C4×Dic3—71no—
250C2×C3×C7—41no—
251C2×C3×C7H(5,𝔽2)11yescharacteristic
252C2×C3×C7H(5,𝔽2)11yescharacteristic
253C2×C3×C7H(5,𝔽2)11yescharacteristic
254D21—41no—
255C3×D7—41no—
256D3×C7—41no—
257D3×C7—41no—
258D3×C7—41no—
259#124—71no—
260#124—211no—
261#124—211no—
262#124—211no—
263#124—211no—
264#124—211no—
265#124—211no—
266#124—211no—
267#124—211no—
268#120—31no—
269#120—211no—
270#120—211no—
271#120—211no—
272#120—211no—
273#120—211no—
274C22×C7—21no—
275C22×C7—21no—
276C22×C7—21no—
277C22×C7—61no—
278C22×C7—61no—
279C22×C7—61no—
280C22×C7—61no—
281C22×C7—61no—
282C22×C7—61no—
283C22×C7—61no—
284C22×C7—61no—
285C22×C7—61no—
286C22×C7—124no—
287C22×C7C23×D311yescharacteristic
288C2×D7—21no—
289C2×D7—21no—
290C2×D7—21no—
291C2×D7—61no—
292C2×D7—61no—
293C2×D7—61no—
294C2×D7—124no—
295C4×C7—21no—
296C4×C7—21no—
297C4×C7—61no—
298Dic7—21no—
299Dic7—21no—
300Dic7—21no—
301Dic7—61no—
302Dic7—61no—
303Dic7—61no—
304C23×C3—71no—
305C23×C3C22×D711yescharacteristic
306C22×D3—41no—
307C22×D3—41no—
308C22×D3—41no—
309C22×D3—71no—
310C22×D3—281no—
311C22×D3—281no—
312C22×D3—281no—
313C22×D3C22×D711yescharacteristic
314C22×D3C22×D711yescharacteristic
315C22×D3C22×D711yescharacteristic
316C3×Q8—281no—
317C3×D4—281no—
318C2×C3×C4—71no—
319C2×C3×C4—71no—
320C2×C3×C4—71no—
321C2×C3×C4C22×D711yescharacteristic
322C2×C3×C4C22×D711yescharacteristic
323#67—41no—
324#67—281no—
325#67—281no—
326#67—281no—
327C2×Dic3—71no—
328C2×Dic3—71no—
329C2×Dic3—71no—
330C2×Dic3C22×D711yescharacteristic
331D12—41no—
332D12—41no—
333D12—281no—
334D12—281no—
335Dic6—281no—
336Dic6—281no—
337C3×C7H(3,𝔽4)11yescharacteristic, complemented, Hall
338C24—31no—
339C24—211no—
340C2×Q8—71no—
341C2×Q8—211no—
342C2×Q8—211no—
343C2×D4—31no—
344C2×D4—31no—
345C2×D4—31no—
346C2×D4—71no—
347C2×D4—211no—
348C2×D4—211no—
349C2×D4—211no—
350C2×D4—211no—
351C2×D4—211no—
352C22⋊C4—31no—
353C22⋊C4—31no—
354C22⋊C4—71no—
355C22⋊C4—71no—
356C22⋊C4—71no—
357C22⋊C4—211no—
358C22⋊C4—211no—
359C22⋊C4—211no—
360C22⋊C4—211no—
361C22⋊C4—211no—
362C22⋊C4—211no—
363C22⋊C4—211no—
364C22⋊C4—211no—
365C22⋊C4—211no—
366C22⋊C4—211no—
367C22⋊C4—211no—
368C22⋊C4—211no—
369C22⋊C4D3×D711yescharacteristic, complemented
370C42—71no—
371C42—211no—
372C42—211no—
373C2×C7—41no—
374C2×C7—121no—
375C2×C7—121no—
376C2×C7—121no—
377C2×C7#100411yescharacteristic
378C2×C7#100911yescharacteristic
379C2×C7#100911yescharacteristic
380D7—41no—
381D7—121no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—141no—
386C22×C3—141no—
387C22×C3—141no—
388C22×C3C23×D711yescharacteristic
389C2×D3—21no—
390C2×D3—21no—
391C2×D3—21no—
392C2×D3—21no—
393C2×D3—21no—
394C2×D3—21no—
395C2×D3—21no—
396C2×D3—21no—
397C2×D3—21no—
398C2×D3—44no—
399C2×D3—141no—
400C2×D3—141no—
401C2×D3—141no—
402C2×D3—284no—
403C3×C4—21no—
404C3×C4—21no—
405C3×C4—141no—
406C3×C4—141no—
407C3×C4—141no—
408Dic3—21no—
409Dic3—141no—
410Dic3—141no—
411Dic3—141no—
412C23—31no—
413C23—31no—
414C23—31no—
415C23—71no—
416C23—121no—
417C23—121no—
418C23—121no—
419C23—211no—
420C23—841no—
421C23—841no—
422C23—841no—
423C23C2×D3×D711yescharacteristic
424Q8—281no—
425Q8—841no—
426Q8—841no—
427D4—121no—
428D4—121no—
429D4—121no—
430D4—281no—
431D4—841no—
432D4—841no—
433D4—841no—
434D4—841no—
435D4—841no—
436C2×C4—31no—
437C2×C4—71no—
438C2×C4—71no—
439C2×C4—71no—
440C2×C4—211no—
441C2×C4—211no—
442C2×C4—211no—
443C2×C4C2×D3×D711yescharacteristic
444C2×C4C2×D3×D711yescharacteristic
445C7#568311yescharacteristic, complemented, Sylow
446C2×C3—41no—
447C2×C3—281no—
448C2×C3#654811yescharacteristic
449C2×C3#654811yescharacteristic
450C2×C3#654811yescharacteristic
451D3—41no—
452D3—41no—
453D3—41no—
454D3—281no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—61no—
459C22—61no—
460C22—61no—
461C22—61no—
462C22—61no—
463C22—61no—
464C22—61no—
465C22—61no—
466C22—61no—
467C22—124no—
468C22—141no—
469C22—141no—
470C22—141no—
471C22—421no—
472C22—421no—
473C22—421no—
474C22—844no—
475C22C22×D3×D711yescharacteristic
476C4—21no—
477C4—21no—
478C4—61no—
479C4—141no—
480C4—141no—
481C4—141no—
482C4—421no—
483C4—421no—
484C4—421no—
485C3#9028511yescharacteristic, complemented, Sylow
486C2—41no—
487C2—121no—
488C2—121no—
489C2—121no—
490C2—281no—
491C2—841no—
492C2#1062156511yescharacteristic
493C2#1062157211yescharacteristic
494C2#1062157411yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D7
commutator, socle, cosocleC22×C3×C7C24
FittingC3×C7×C22⋊C4C22
hypercenterC22⋊C4D3×D7
hypocenterC3×C7H(3,𝔽4)
LCSG ▷ C22×C3×C7 ▷ C3×C7
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #10621368C2semidirect
2. C7×#882C2semidirect
3. C3×#6448C2semidirect
4. #10621139C2semidirect
5. #10621132C2semidirect
6. #10621130C2semidirect
7. #10621087C2semidirect
8. #10621037C2semidirect
9. #10621037C2semidirect
10. #10621026C2semidirect
11. #10621024C2semidirect
12. #10620935C2semidirect
13. #10620932C2semidirect
14. #10620912C2semidirect
15. #10620888C2semidirect
17. C23×D3×C7C22semidirect
18. C22×D3×D7C22semidirect
20. C2×Dic42C22semidirect
25. C2×C3×Dic14C22semidirect
26. C2×#4248C22semidirect
31. C3×C7×C22⋊C4C22semidirect
32. #66636C22semidirect
33. #66631C22semidirect
34. #66631C22semidirect
35. C4×Dic21C22semidirect
36. C7×(C2×D3)⋊C4C22semidirect
37. C7×(C2×D3)⋊C4C22semidirect
38. C3×C22⋊Dic7C22semidirect
39. C3×(C2×D7)⋊C4C22semidirect
40. C3×(C2×D7)⋊C4C22semidirect
41. C3×C4×Dic7C22semidirect
42. #66575C22semidirect
43. (C2×D3)⋊Dic7C22semidirect
44. (C2×D3)⋊Dic7C22semidirect
45. (C2×D3)⋊Dic7C22semidirect
46. (C2×D3)⋊Dic7C22semidirect
47. (C2×D3)⋊Dic7C22semidirect
48. (C2×D3)⋊Dic7C22semidirect
49. (C2×D3)⋊Dic7C22semidirect
50. (C2×D7)⋊Dic3C22semidirect
51. Dic3×Dic7C22semidirect
66. #6448D3semidirect
114. C2×Dic14C2×D3semidirect
117. C7×C22⋊C4C2×D3semidirect
126. C22⋊Dic7C2×D3semidirect
131. (C2×D7)⋊C4C2×D3semidirect
132. (C2×D7)⋊C4C2×D3semidirect
135. C4×Dic7C2×D3semidirect
148. #882D7semidirect
216. C23×D3C2×D7semidirect
232. C3×C22⋊C4C2×D7semidirect
246. (C2×D3)⋊C4C2×D7semidirect
247. (C2×D3)⋊C4C2×D7semidirect
337. C3×C7H(3,𝔽4)semidirect
369. C22⋊C4D3×D7semidirect
445. C7#5683semidirect
485. C3#90285semidirect

Maximal subgroups

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

subgroupindex
#106213682
C7×#8822
C3×#64482
#106211392
#106211322
#106211302
#106210872
#106210372
#106210262
#106210242
#106209352
#106209322
#106209122
#106208882
#902853
#56837